Some remarks on the blow-up rate for the 3D magnetic Zakharov system

Autor: Yansheng Ma, Ting Zhong, Zaihui Gan
Rok vydání: 2015
Předmět:
Zdroj: Journal of Functional Analysis. 269:2505-2529
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2015.07.010
Popis: We continue our study [8] on the Cauchy problem for the three-dimensional magnetic Zakharov system (ZSM){iEt+ΔE−nE+i(E∧B(E))=0,nt=−∇⋅V,Vt=−∇n−∇|E|2,ΔB−iη∇×∇×(E∧E‾)+δB=0, with initial data (ZSM-1)E(0,x)=E0(x),n(0,x)=n0(x),V(0,x)=V0(x). Let (E,n,V)∈C([0,T),H1(R3)×L2(R3)×L2(R3)) be a blow-up solution to the Cauchy problem (ZSM)–(ZSM-1), and let T1e, e∈(0,14] and q=32(1−e)∈(32,2]. The estimate (E-1) implies that, for a
Databáze: OpenAIRE
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